QualPro Recommendations for

QualPro Recommendations for
ACT Test Score Improvement for East Tennessee School Systems

QualPro General Recommendations*
Ensure students learn key vocabulary words Ensure students use better test-taking strategy for reading and science reasoning Ensure students learn some essential math concepts Ensure that the students take at least four practice exams * These recommendations should be accomplished during the students’ junior year.

Ensure Students Learn Key Vocabulary Words
Most students can’t score well because they don’t understand a lot of the words on the four components of the ACT. We have identified the words that East Tennessee students have the most trouble with.

Ensure Students Use a Better Test-Taking Strategy for Reading and Science Reasoning
For reading and science reasoning, the answers are in the test. Based on our previous work with East Tennessee students, the best test-taking strategy is to go immediately to the questions and then quickly find the answers. DO NOT follow the ACT instructions which says to read the passages and study the graphs and then try to answer the questions.

Ensure Students Learn Some Essential Math Concepts
Pre-algebra Elementary algebra Intermediate algebra Coordinate geometry Plane geometry Trigonometry Miscellaneous topics Math test-taking strategy

We feel confident that any high school that follows this program will increase their average ACT Scores by at least three points.

QualPro’s Experience Improving ACT Test Scores
Group 1 Eighteen high school baseball players from East Tennessee Group 2 Students from Sevier County High School

Group 1 ACT Test Score Improvement
23.1 19.4 Average ACT Score for 18 Baseball Players

Group 2 ACT Test Score Improvement
ACT Category

Group 2 Composite ACT Test Score Improvement
ACT Composite

ACT Test Prep English

ACT Vocabulary — Words Required for English and Reading Tests
ACT Vocabulary — Words Required for English and Reading Tests* (Bare Minimum) abstract absurdity acknowledge acute aesthetic affluence agenda allegedly ambiguity ample analogy anomaly apathy arbitrary articulate (v) assert assertion authoritative auxiliary breadth chaos chronic chronological cite coherence coherent collaborating commendable compellingly concede concise concrete (adj) condescension confer conformity connote consequence consequently consistent contemporary (n) context controversial conversely convey correlate (v,n) cosmopolitan (adj) counter (v) criterion cryptic daunting defiantly definitive delete deletion denote derive detached deterrence detract dialect dilemma diligent discern disdainful dispel dissonance distract diverse drawback dry (humor) eclectic editorial (adj) eloquent eminent emphatically enumerate escapist establishment evaluative evoke explanatory explicit extent façade facet factual faculty feign fictional fictitious figuratively finding (n) foresight formality format frenzied frivolous furthermore generalities generalization generalize generate genre glib humanitarian hypothesis idealistic ideological idiomatic illogical illustrative imminent implication imply impose inaccurate inadvertently incentive inclination inconsistency inconstant indication indifference inevitable inexplicably infer inference influential ingenious ingenuous inherent initial (adj) inquiry insight insignificant insinuate insistently insufficient intent intently interpretation intolerant intricacies intricate intrigue (v) irreconcilable irrelevant irrevocable likewise longstanding lyricism mainstream mandate (v) matter of course means (n) mediocre melancholy mere meticulous minuscule mischievous misconception momentous mutual narrative nevertheless nonetheless nostalgia noteworthy notion obscure (v) obtuse omission omit on behalf of one-dimensional onus outset paradox parenthetical perceptual phenomenal philosophy plagiarism populace populous portray preceding precisely preconceived previous progressive quasi- quintessential randomly rational redundancy redundant reinforce relevant reluctantly remnant remote replenish resemblance resistant resolution resonate resources respectively revel reverent revisionist rift rudimentary sacrilege sanctuary sapling satellite saturation scholarly scrunity scrutinize seascape seemingly selectively seminal sensory sentiment serenity shrill shrub shun simultaneous singular site sit-in sizable skepticism slogan social order solace sovereign specific speculate spin-off stable stationary stationery status steerage stereotypical stifle subjective succession succumb superficial superimpose sustenance syndicated syringe taut taxed with tenet terra firma terrestrial theorize thereafter thus timber tirade toxin trajectory transcend transition translucent treason typesetting tyranny tyrant uncanny unparalleled unprecedented unsolicited urgency urn vaccine vindicate visionary vivid voluptuous vulnerable wherefore whimsy withdrawn worldview * All these words taken from the five practice tests in the real ACT Prep Guide, 3rd Ed. These are words that the students are REQUIRED to know just to process the answers

ACT Test Prep Reading

Ensure Students Use a Better Test-Taking Strategy for Reading and Science Reasoning
For reading the answers are in the test. Spend one minute skimming the passages. Go immediately to the questions and then quickly find the answers. DO NOT follow the ACT instructions which says to read the passages and then try to answer the questions.

ACT Test Prep Math

Goal: Answer 70% correctly (42 out of 60)
Math Section of the ACT 60 Questions in 60 Minutes Goal: Answer 70% correctly (42 out of 60) This means you need a strategy to confidently answer 42 questions correctly in 60 minutes.

Math Section Content Math vocabulary Pre-algebra Elementary algebra
Intermediate algebra Coordinate geometry Plane geometry Trigonometry Miscellaneous topics Test-taking strategy

Math Vocabulary area of a circle chord circumference collinear
complex number congruent consecutive diagonal directly proportional endpoints function y = R (x) hypotenuse integer intersect irrational number least common denominator logarithm matrix mean median obtuse perimeter perpendicular pi polygon prime number quadrant quadratic equation quadrilateral quotient radian radii radius rational number real number slope standard coordinate plane transversal trapezoid vertex x-intercept y-intercept

ACT Test Prep Science

The Percent Correct Versus Science Score

Answer 30 out of 40 (75%) of questions yields a score of 24 on the Science Reasoning portion of the ACT

Science Section of the ACT
40 Questions in 35 Minutes Goal: Answer 75% correctly (30 out of 40) This means you need a strategy to confidently answer 30 questions correctly in 35 minutes.

Science Reasoning Vocabulary
2-butanone 2-propanol µmho/cm [theta] absorbance Alpha, alpha decay amino acid ammonium nitrate asteroid average molecular mass beta beta particles biomass biosphere biotic index bog buoyancy buoyant force calcareous ooze calcite calcium carbonate capacity capillary carbon dioxide carbon particles carbonate Celsius charged particles chromatid chromosome climatic colorimeter comet condensation conductivity continental drift continental ice sheet crater crown fire cytoplasm °C CaCl₂ CaCO CaCo₃ Ch³ CuO denature density depth range derived diffuse directly proportional drawn to scale ∆ δ ecology ecopark ecosystem efficiency emit equilibrium equivalency erosion ethyl acetate exclusion chromatography extinct extinction Fahrenheit failed burn flask formula frequency °F ft/sec gamma gas chromatograph genus glacier groundwater habitat helium hexane high-frequency H₂ H₂O Hg ice shelf ignite index infrared inorganic invertebrate isotope joule kinetic km landmass lava lithium chloride long-term LiCl mammal manometer mapping function marine (adj) Mass, massive meiosis mesopause mesosphere Methane, methanol microscopy migrating migratory Milli-bar model Mole, molecule molecular weight montane mL, mm Hg, µ nitrite nitrogen-fixing nonreactive numerical aperture nutrient NaCl, NH₄NO₃ objective lens organic matter organism osmosis ozone paleozoic particle parts per million peat peer (n) permeable photosynthetic pinnate plume plunger plutonium polar pollen polymer polyrhythm polystyrene pore water precipitate (v) projectile prophase pyrotechnics radar pulse radioactive decay rallies (n) range reaction reactive recasting recipient relief supplies renatured retention time (RT) Revitalize rift saturation

Science Reasoning Vocabulary
sea floor sediment seemingly selective semipermeable sluggishly sodium chloride solar solar system solute (adj) solutes solution Solvent sparking device species specific specific gravity speculate spent sprawl spurred stagnant standard atmospheric pressure standard sample static stratopause stratosphere sucrose sulfate supersaturated suspension synthesis synthesize SO₄ tactic thermosphere tolerance toxic tropopause troposphere ultraviolet undersaturated uninhibited uranium series vapor vapor plume variable velocity vertebrate volcanic volcanism water table watt wetlands zoning Scientific notation Students should recognize: allele notation binomial nomenclature chemical equation chemical formula element symbol isotope

We feel confident that any high school that follows this program will increase their average ACT Scores by at least three points.

Appendix 1 ACT Vocabulary Words Required for English and Reading Tests—Bare Minimum

ACT Vocabulary — Words Required for English and Reading Tests
ACT Vocabulary — Words Required for English and Reading Tests* (Bare Minimum) abstract absurdity acknowledge acute aesthetic affluence agenda allegedly ambiguity ample analogy anomaly apathy arbitrary articulate (v) assert assertion authoritative auxiliary breadth chaos chronic chronological cite coherence coherent collaborating commendable compellingly concede concise concrete (adj) condescension confer conformity connote consequence consequently consistent contemporary (n) context controversial conversely convey correlate (v,n) cosmopolitan (adj) counter (v) criterion cryptic daunting defiantly definitive delete deletion denote derive detached deterrence detract dialect dilemma diligent discern disdainful dispel dissonance distract diverse drawback dry (humor) eclectic editorial (adj) eloquent eminent emphatically enumerate escapist establishment evaluative evoke explanatory explicit extent façade facet factual faculty feign fictional fictitious figuratively finding (n) foresight formality format frenzied frivolous furthermore generalities generalization generalize generate genre glib humanitarian hypothesis idealistic ideological idiomatic illogical illustrative imminent implication imply impose inaccurate inadvertently incentive inclination inconsistency inconstant indication indifference inevitable inexplicably infer inference influential ingenious ingenuous inherent initial (adj) inquiry insight insignificant insinuate insistently insufficient intent intently interpretation intolerant intricacies intricate intrigue (v) irreconcilable irrelevant irrevocable likewise longstanding lyricism mainstream mandate (v) matter of course means (n) mediocre melancholy mere meticulous minuscule mischievous misconception momentous mutual narrative nevertheless nonetheless nostalgia noteworthy notion obscure (v) obtuse omission omit on behalf of one-dimensional onus outset paradox parenthetical perceptual phenomenal philosophy plagiarism populace populous portray preceding precisely preconceived previous progressive quasi- quintessential randomly rational redundancy redundant reinforce relevant reluctantly remnant remote replenish resemblance resistant resolution resonate resources respectively revel reverent revisionist rift rudimentary sacrilege sanctuary sapling satellite saturation scholarly scrunity scrutinize seascape seemingly selectively seminal sensory sentiment serenity shrill shrub shun simultaneous singular site sit-in sizable skepticism slogan social order solace sovereign specific speculate spin-off stable stationary stationery status steerage stereotypical stifle subjective succession succumb superficial superimpose sustenance syndicated syringe taut taxed with tenet terra firma terrestrial theorize thereafter thus timber tirade toxin trajectory transcend transition translucent treason typesetting tyranny tyrant uncanny unparalleled unprecedented unsolicited urgency urn vaccine vindicate visionary vivid voluptuous vulnerable wherefore whimsy withdrawn worldview * All these words taken from the five practice tests in the real ACT Prep Guide, 3rd Ed. These are words that the students are REQUIRED to know just to process the answers

ACT Vocabulary Words Required for English and Reading Tests—Bare Minimum—Comprehensive List
abstract adj—not like anything physical; not representing a physical object; related to thought or imagination as opposed to nature. Opposite of concrete. The two-year-old’s finger painting looked more like abstract art than a picture of a cow. absurdity n—the state of being ridiculously impossible Expecting Charles Barker, the retired basketball player, to wear a pink sequined tutu and walk a tight wire strikes me as the height of absurdity. acknowledge vt—to admit to be true Myra acknowledged that the grapes in the refrigerator would be colder than the ones on the counter. acute adj— 1. in geometry, less that 90° and therefore pointed and sharp; keen My Uncle Theo has an acute sense of humor. 2. immediate and in need of attention; said of a disease. Opposite of chronic Paul was rushed to the hospital for an acute appendix attack. aesthetic adj—artsy; related to beauty or excellence Japanese food is usually more aesthetic than Granny’s home cooking. n—a standard for judging something’s goodness The judge’s aesthetic for rating the divers included the height of the splash as well as the straightness of the divers’ legs. affluence n—wealth Most Americans do not appreciate their affluence when compared to the rest of the world. agenda n—plan of accomplishments and the time needed to perform them I did not have “stop at Bruster’s for ice cream” on my agenda, but I’m glad to add it.

ACT Vocabulary Words (continued)
allegedly adv—according to what people say but unproven By the time you read this, the scandalous things people have allegedly done today will either be proved or disproved. ambiguity n—ability to be understood in either of two ways The Kinks’ song “Lola” was famous for its ambiguity: “I know I’m not the most masculine man,/ But I know what I am, and I’m glad I’m a man / And so’s Lola.” ample adj—adequate; plentiful; abundant If the pants are too short, there is ample fabric in the hem to lengthen them. analogy n—comparison; a way to show how one thing is like another Calling Cruella DeVille’s heart as cold and hard as a diamond is a good analogy. anomaly n—something that doesn’t fit or belong and can’t be explained The doctor was worried about an anomaly in Granny’s heart rhythm. apathy n—lack of feeling My little brother had nothing but apathy for the socks he got for Christmas. arbitrary adj—chosen at random; having no pattern After trying to follow Pia’s singing, Chuck gave up and started playing arbitrary chords. articulate v—to say something clearly and in detail Ms. Hall articulated to the noisy class that even a sigh would cause them to miss recess. assert vi—to state strongly Aunt June asserted that her peach pie always won the prizes at the fair. assertion n—a statement made strongly When Mike ate his pencil eraser, I believed his assertion that he was hungry. authoritative adj—confident; sounding as if an expert had said it Anything Dolly Parton says about wigs is considered authoritative advice. auxiliary adj – additional; used as a substitute in case of need Our home has an auxiliary power source in case we lose electrical service. breadth n—width, wide range or extent During the debate, the challenger demonstrated his breadth of experience in foreign affairs. © 2012 QualPro

chaos n—complete confusion or disorder The chaos that occurred after the hurricane included young men overturning vehicles, rioting, and looting. chronic adj—ongoing; across time. Opposite of acute Because my sister suffers from chronic headaches, she had to give up soccer. chronological adj—arranged in date or time order Jacob’s diary provided a chronological account of his life. cite v—to show the source of My teacher makes us cite all our sources when we write a research paper. Note: do not confuse with site coherence n— logical connection and clearness Dr. Hackney’s coherence on the witness stand caused the jury to believe her testimony. coherent adj—logically connected My English teacher insists that a paragraph must include a good topic sentence and several coherent supporting sentences. collaborating vi—to work together with The music, dance, and art departments are collaborating with the drama department to produce Oklahoma. commendable adj—worthy of praise We want to thank the art department, whose commendable work made our stage look like a wide-open prairie. compellingly adv—in a manner that causes someone to consider believing Because Joan presented her argument so compellingly, Mom let her go on spring break. concede vt—to admit Although the race was close, the losing candidate conceded defeat just before midnight. concise adj—efficient with words; saying what needs to be said in as few words as possible. Being concise makes sense when sending a telegram that charges by the word. © 2012 QualPro

concrete adj—looking like something physical; representing a physical object; related to nature, as opposed to thought or imagination. Opposite of abstract. Most people believe concrete evidence more than they believe gossip. condescension n—the act of lowering oneself to do something considered too “low” The movie star acted with condescension to her old school chums, who had known her when she was a second-string basketball player. confer vi—to talk with on a particular subject After the coach conferred with the referee, he took Calvin out of the game. conformity n—the act of going along with what everybody else is doing The rule at my school is conformity for the first three years, then everyone dresses as they please. connote vt—to cause to think about, as opposed to plainly stating. Opposite of denote. To many people, country music connotes cowboy boots, glittery clothes, and twangy voices. consequence n—result; what follows due to something that went before The consequence of going overboard with your credit card is a mountain of debts. consequently adv—as a result We have had little rain this summer; consequently, many crops are drying up. consistent adj— 1. the same throughout; fair Old Man Turner is mean, but at least he’s consistent; he yells at everybody. 2. in harmony; having the same principles The kids’ new club rules are consistent with the Constitution. contemporary n—someone who lived at the same time Napoleon and Jane Austen were contemporaries, but I don’t think they ever met. context n—the sentence that surround the words Depending on the context, a “run” may be a point in baseball or a tear in a woman’s stocking. controversial adj—causing much discussion or scandal Letting eighteen-year-old soldiers drink alcohol is still controversial; they can give their lives for their country, but they can’t buy a drink to celebrate a victory. © 2012 QualPro

conversely adv—in the opposite order Mom always puts milk first, then butter, then eggs in the refrigerator; conversely, she always removes eggs first, then butter, then milk. convey vt—to make known; to serve as a means of communication By his tears, DeShawn conveyed that the movie touched his heart. correlate vt—to show how one thing relates to another My favorite teacher can correlate what students like with what they need to learn. cosmopolitan adj—worldly; educated in the ways of the world Adding options like salsa, guacamole, and mushrooms gave Uncle Larry’s hot dog stand a cosmopolitan air. counter vt—to oppose in response When my brother said I didn’t know everything, I countered with, “Neither do you!” criterion n—a standard or reason for judgment. Bubba’s criterion for a good car is a teeth-rattling sound system, but Brad’s criteria are good mileage, rapid acceleration, and a color that matches his eyes. Note: the plural is criteria. cryptic adj—with a hidden meaning (its root word is crypt, meaning “hiding place”) Because Beth always gives me a cryptic answer, I’m never sure what she wants. daunting adj—big or scary enough to make a person think twice before going ahead Nichole had a daunting amount of homework, but she finished it before 9:00. defiantly adv—with an oppositional attitude. Patrick Henry defiantly said, “Give me liberty or give me death.” Note: do not confuse with definitely. definitive adj— 1. the qualities that make something what it is The quarterback’s definitive coordination earned him a full scholarship. 2. the most nearly complete and accurate In Myra’s family, her mother’s rules are the definitive rules. Note: do not confuse with definite. © 2012 QualPro

delete vt—to take out; remove (said of words) To make sure the handout of the Pledge of Allegiance was perfect, Gilda told Fred to delete “Richard Stands” and write “which it stands” instead. deletion n—the act of marking something out The boss made so many deletions that it would have been easier for me to start over. denote vt—to state plainly; to give an exact meaning. Opposite of connote. The “six-pack” my sister’s computer date bragged about was actually what it denoted— a half-dozen cans of Pepsi, not a muscular abdomen! derive vt—to arrive at by computing or thinking My big sister derives a lot of pleasure from watching my brother and me arguing. deterrence n—something that keeps people from doing something All those thorns provide deterrence against the theft of Mrs. Lorrimer’s prize roses. detached adj—neither on one side nor the other; objective; without bias; not “attached” to one side of an argument The policeman’s detached attitude made me believe he was listening to me fairly. detract vi—to reduce the quality of Jeremy’s handprints in the frosting detract from the eye appeal of his birthday cake. dialect n—a form of language used by people of a certain region or group Having always lived in East Tennessee, Ashley understood the dialect of the South. dilemma n—a choice between two confusing alternatives Madison was faced with the dilemma of losing sleep to study for the test or getting eight hours’ sleep but not reading the last two chapters. diligent adj—hard-working It wasn’t so much being smart as it was being diligent that earned Steve his first million. discern vt—to recognize as separate or different A smart daughter will discern her mother’s mood before she asks to stay out late. © 2012 QualPro

disdainful adj—showing lack of respect The student’s disdainful behavior caused the entire class to miss recess. dispel vt—to get rid of Harold’s performance in his latest movie dispelled the rumors that his success is due to his famous father. dissonance n—unmatched, disturbing sounds; lack of harmony There is too much dissonance between Butch’s Butcher Shop and Veronica’s Vegan Deli for them to share a courtyard. distract vt—to draw attention away Listening to hip hop while I study distracts me from my French homework. diverse adj—having parts that are unlike each other The Mortons have diverse pets: a hermit crab, a Great Dane, and a chicken. drawback n—disadvantage of doing something; reason not to do something One big drawback to being a medical examiner is the smell of the dead bodies. dry adj—reserved and subtle, as opposed to broad and obvious (said of a sense of humor) Steven Wright’s dry humor leads him to write jokes like, “Right now I'm having amnesia and déjà vu at the same time. I think I've forgotten this before.” eclectic adj—having components from a wide variety of sources Maeve’s new living room is an eclectic mix of Louis XIV furniture, Disney character posters, and lamps made from cowboy spurs, saddles, and ropes. editorial adj—having the qualities an editor might add, as opposed to fact-based news stories Mr. Franklin’s editorial comments made it clear that his newspaper would not be supporting Taft in the fall. eloquent adj—graceful and skillful of speech The committee chose Thomas Jefferson to write the Declaration of independence because he had written so many eloquent letters and proposals before. eminent adj—famous; outstanding The eminent surgeon, Dr. Phillip Easterly, spoke at my sister’s graduation. Note: often confused with imminent © 2012 QualPro

emphatically adv—with great emphasis When the waiter asked Ted if he wanted anchovies, Ted emphatically said, “No!” enumerate vt—to count out one by one Carl enumerated Melissa’s charms: her eyes, her figure, and her quiet sense of humor. escapist adj—literature or art that rejects the routine of the real world Arliss and Ethan prefer escapist video games with dragons and wizards to playing ball. establishment n—“The powers that be”—those who by their wealth or power make the social rules The hippies rebelled against the Establishment by wearing long hair and blue jeans. evaluative adj—helping to judge The news is not supposed to be evaluative; it’s supposed to give information so that the viewers can make up their own minds. evoke vt—to bring to the mind or the senses The smell of hot buttered popcorn always evokes a dark theatre and a new movie. explanatory adj—explaining; giving details about something in order to make it easier to understand The recipe made more sense when Madison read the explanatory notes at the bottom. explicit adj—obvious and detailed The crime scene show was too explicit to watch while we were eating pizza. extent n—a place as far as People appreciate how hard people work for them only to the extent that they have done the job themselves. façade n—false face; front; shallow covering of the real thing Driving a fancy car was part of the façade that hid how poor he really was. facet n—a particular side, as of a jewel; aspect When Nat saw the photo of “The Pirates of Penzance” in his father’s yearbook, he appreciated a new facet of his father’s personality. factual adj—based on proven knowledge The skid marks provided factual evidence that the driver had tried to stop. © 2012 QualPro

faculty n—individual parts that make up a whole person or institution The school’s faculty, every single one of the teachers, reminded Tommy of the faculties he had left after his blindness: memory, imagination, sense of humor, intelligence, and understanding. feign vt—to pretend; to fake Steve feigned sleep so his mother would leave him alone. fictional adj—made up, as opposed to factual The Wizard of Oz is a fictional character. fictitious adj—made up, as opposed to factual Oz is a fictitious country. figuratively adv—in a way; so to speak; in a way that people understand but not literally true Jodi Lee is a ray of sunshine at the retirement home, figuratively speaking. finding n—what someone has found after much research. Usually plural: findings In spite of all the findings, cigarette companies still say smoking does not cause cancer. foresight n—the ability to understand beforehand, to “foresee” With great foresight, Howie took his rain boots and his dusk goggles on vacation. formality n—“dressed-up”-ness; the degree to which something follows social rules Because of the formality of the courtroom, I decided not to wear cutoffs. format n—shape, size, and general arrangement of a book, magazine, or other presentation Granddaddy has trouble learning the format of his new iPhone. frenzied adj—with hysterical agitation; wild The middle school girls had a frenzied attack on the latest teen idol. frivolous adj—not serious; silly The dress had a frivolous bunny made out of ruffles on one sleeve. furthermore adv—in addition Purple is not a color that brides wear; furthermore, it’s not my favorite color. generalities n—the big ideas or qualities that smaller ideas share The candidate spoke in generalities but never gave a single specific fact. © 2012 QualPro

generalization n—an overall big idea drawn from a bunch of smaller ideas Grandma’s generalization that all rock stars have long hair is no longer true. generalize vi—to state the qualities that different things or ideas have in common To generalize that all skaters are rebellious slackers is unfair. generate vt—to cause to be made That lemonade stand of Jerry’s generated $120 in only one hour. genre n—category The horror film genre is not the only kind Stephen King’s books have inspired. glib adj—quick-witted; smooth-tongued Any glib salesman can sell anything to Aunt Becky. humanitarian adj—having to do with those who serve mankind Although being a billionaire takes a lot of time, Bill Gates is involved in many humanitarian efforts, like teaching adults to read. hypothesis n—the unproven idea you start out with before you prove something Greg tested his hypothesis that his sister was sneaking out at night by watching her. idealistic adj—expecting the best; identified by ideals, rather than dreads “The Sun’ll Come Out Tomorrow” from Annie is one of the most idealistic songs I know. ideological adj—having to do with ideas, their nature and source The differences between those two politicians aren’t personal; they are ideological. Idiomatic adj—unique in language and thought; setting its own standard Mama Lizabetta’s English is idiomatic, but all the grandkids know what she means. illogical adj—lacking logic; not making sense Washing your hair right before you go swimming in the lake is illogical. illustrative adj—so descriptive that it draws a mental picture The speaker’s examples of the beach were so illustrative that I could almost hear the ocean. imminent adj—on its way; about to arrive The weatherman says rain is imminent, so take your umbrella. Note—often confused with eminent © 2012 QualPro

implication n—the idea a person gives without saying it directly When three people offer you a Tic-Tac, the implication is that you’ve got bad breath. Note: different from inference imply vt—to give an idea indirectly, without coming out and saying When Brian offered Hugo a bigger chair, he was implying that Hugo was overweight. Note: different from infer impose vt—to cause unnecessary trouble to “It‘s after midnight, Mrs. Kane, so we won’t impose in you any longer. Good night.” inaccurate adj—wrong; faulty After the ball game was rained out, it was obvious that Channel 9’s weather report prediction of 100% sunshine was inaccurate. inadvertently adv—without having been planned; by not being careful The waiter inadvertently knocked the cherry off my sundae when he reached for the dirty plate. incentive n—a reward or prize offered to get someone to behave a certain way Hanging a nice, juicy carrot in front of a donkey’s nose is a good incentive to make him move forward. Inclination n—leaning; tendency Two of the Gregory children show a definite inclination towards music. inconsistency n—lack of “sameness”; difference in substance or texture Waiter, there is an inconsistency between what I ordered and what you brought me. inconstant adj—unsteady; wavering Walter, that jerk, is an inconstant boyfriend; he dates three girls besides Jodi. indication n—hint; sign With a tilt of her head, Kiki made an indication that she wouldn’t mind talking to Bob. Indifference n—absence of caring Whether you go or stay is a matter of complete indifference to me. inevitable adj—unavoidable One inevitable result of eating dessert at every meal is weight gain. © 2012 QualPro

inexplicably adv—“un-explain-ably” “Nobody broke the vase, Mom,” Jimbo said. “It just inexplicably shattered into a million pieces.” infer v—to come up with an idea based on what someone said When Lee handed me a comb, I inferred that my hair looked messy. Note: different from imply inference n—an idea that comes from what someone else said When I saw Nana looking under the bed, my inference was that she had lost something. Note: different from implication influential adj—having influence; having “pull” The Beatles were highly influential in the recording industry, being the first to make their own technical decisions. ingenious adj—clever and inventive My little brother developed an ingenious way to let the dog out without leaving the sofa. Note: often confused with ingenuous ingenuous adj—innocent, trusting, simple “Why does Buck like to look at the girls in the short skirts, Daddy?” the ingenuous little girl asked. Note: often confused with ingenious inherent adj—built-in naturally While vitamin pills can be useful, the vitamins inherent in fresh vegetables are healthier. initial adj—first; at the beginning At our initial meeting, Van seemed boring; when I knew him better, though, he made me laugh. inquiry n—question-asking The police’s inquiry into the robbery revealed nothing except that the thief had red hair. insight n—ability to see or understand the inner nature Although she’s eighty-three, Nana has a lot of insight into the problems of teenage girls. insignificant adj—unimportant; too small to matter Except for a few insignificant details, Gina had finished planning the entire wedding. © 2012 QualPro

insinuate vt—to hint or suggest indirectly When Marcy looked at me and locked her desk, she was insinuating that I was nosy. insistently adv—refusing to give up The salesman insistently knocked at the door until Grandpa wheeled his wheelchair to the door and answered. Insufficient adj—not enough The police announced that they had insufficient evidence to make an arrest. intent adj—determined to; focused Grace was so intent on following the traffic laws that she did not notice what Luke was saying. n—purpose By bringing Kate a dozen roses, Bill’s intent was to express his love, not to make her sneeze. intently adv—with great concentration The boys played Masters of Destruction so intently that they did not hear Mom call them for dinner. interpretation n—way of saying something in a different language or for a different listener A Sesame Street interpretation of Shakespeare’s play Romeo and Juliet would probably leave out the deaths. intolerant adj—unwilling or unable to put up with Since Donna is intolerant of milk products and Uncle Todd is intolerant of hippies, they did not attend the opening of the new Woodstock Ice Cream Parlor. intricacies n—complicated details Caitlyn hates to dust around the intricacies of her mother’s miniature glass animal collection. intricate adj—delicate and complicated Norman has no problem with the intricate workings of the inside of a computer. intrigue vt—to fascinate Uncle Steve told Quint, “No matter how old I get, the mind of a woman will always intrigue me.” © 2012 QualPro

irreconcilable adv—un-matchable; that cannot be brought into agreement Since Matt bred beef cattle and Kiki was a vegetarian, their differences were irreconcilable. irrelevant adj—unrelated; not important to the matter at hand Whether you pay me back with two five-dollar bills or ten ones is irrelevant, as long as you pay me back today. irrevocable adj—unchangeable Dad’s decree that no daughter of his will date until she is fifteen is final and irrevocable. likewise adv—in the same way Her friends like Jane because she’s so positive; likewise, strangers like her for her friendliness. longstanding adj—having been established a long time Some of the council members were uneasy changing the longstanding town boundaries. lyricism n—graceful, musical quality Even voters who disagreed with his views were swayed by the lyricism of his speeches. mainstream n—majority; common idea The vegans want Friday to be Tofu Day, but kids in the mainstream want it to stay Pizza Day. mandate v—to cause to be demanded The alarming increase in stray dogs mandated a crackdown by the Humane Society. matter of course n—thing that people just accept without thinking Mom began washing the dishes as a matter of course, even though it was Mother’s Day. means n—stuff needed; way I had the need and the desire to buy a car, but not the means, so I got a job. mediocre adj—neither high- nor low-quality; in-between; average The pie was mediocre; it wasn’t as delicious as Granny’s, but it wasn’t as nasty as mine. melancholy adj—sad and thoughtful; gloomy Rainy days like this make me so melancholy that I need to watch a good comedy. © 2012 QualPro

mere adj—only; nothing more or other than Nobody expected that a mere five-year-old could play the piano like Elton John. meticulous adj—picky and extremely careful The guy who washes my car is so meticulous that he goes over the interior with a Q-tip. minuscule adj—very tiny Grandpa didn’t see the minuscule insect on his potato salad before he put it in his mouth. mischievous adj—fond of playing jokes and causing harmless trouble Both puppies and kittens can seem mischievous because of their curiosity. misconception n—mistaken idea After she saw the mail deliverer put the mail in the mailbox, Jenna got the misconception that he wrote all the letters, bills, and catalogues. momentous adj—important in a life-changing way The invention of the electric light bulb was a momentous step in modern civilization. mutual adj—as much from one side as the other; agreeable to both sides; from both sides Buzz likes Liz, and Liz likes Buzz; their feelings are mutual. narrative n—the telling of a story Barack Obama’s narrative includes growing up in a single-parent family. nevertheless adv—unlike what you might expect; nonetheless I slept for nine hours; nevertheless, I was still tired. nonetheless adv—unlike what you might expect; nevertheless Sam was careful; nonetheless, he spilled the coffee. nostalgia n—an emotional feeling about the past When the movie Grease came out in the 1970s, America felt nostalgia for the 1950s. noteworthy adj—worth paying attention to The only noteworthy event from my week at camp occurred when the pool caught fire. notion n—small part of an idea Madison had no notion that the surprise party was for her. © 2012 QualPro

obscure adj—hard to find Sophie was shocked to find an obscure law saying that a husband could not beat his wife with a stick any larger than his thumb. vt—to hide Unfortunately, the clouds obscured the full moon. obtuse adj—dull; not sharp; said of an angle that is greater than 90° because it isn’t “sharp” Because Ryan was so obtuse, Jill and Sam had to come out and tell him they wanted to be alone. omission n—the leaving out of something Due to a famous omission, one version of the Bible said, “Thou shalt commit adultery.” omit vt—to leave out If you omit the eggs when making meat loaf, it won’t stick together. Don’t ask me how I know! on behalf of prep—for the sake of; to represent Kayla gave Ms. Prosser a box of chocolates on behalf of all the students she tutored after school. one-dimensional adj—having neither depth nor width; a spot only, without any development Even though everyone likes him, the Road Runner is a one-dimensional character. onus n—burden Although the fashion world makes being too skinny seem glamorous, the onus of teaching girls to have a healthy view of their bodies is on their parents. outset n—beginning; the place from which one “sets out” I never liked Gordy, even from the outset of his relationship with Sheila, and I was right. paradox n—the relationship between two statements that do not seem to be able to be true at the same time The novel Catch-22 was based on the paradox that you had to be crazy to get out of the army, but you had to be crazy to be in the army in the first place! © 2012 QualPro

parenthetical adj— 1. inside parentheses: words inside curved marks (like those around these words) Takesha’s play is full of parenthetical instructions that tell the actors how to say the lines. 2. that which is said off to the side; not the main idea but one that is worth sneaking in Christi was famous for her parenthetical comments, as when she said, “Lowell, that new teacher, the one you said that looks like Taylor Swift, wants to see you.” perceptual adj—relying on the senses, as opposed to the mind Watching a spinning black-and-white spiral can cause perceptual confusion. phenomenal adj—like nothing else; unique Most fans thought Avatar was a phenomenal movie. philosophy n—way of thinking that guides other thoughts and actions Unfortunately, the philosophy of many tobacco companies is to make as much money as possible, with no regard for the health of their customers. plagiarism n—the using of someone else’s words or ideas without giving that person credit; stealing words or ideas Rob claimed that it was coincidence, not plagiarism, that explained why his report was identical to Fred’s. populace n—the people of a region or group To most Westerners’ surprise, the populace of Indonesia is mostly Muslim. Note: often confused with populous populous n—having a large population New York City is far more populous than Knoxville. Note: often confused with populace portray vt—to display from a certain viewpoint Val Kilmer portrayed Batman as a darker character than the Batman of the 1960s. preceding adj—the one that went before; previous The last tournament was much more exciting than the preceding ones. precisely adv—exactly Whether everyone has arrived or not, Aunt Lois always serves dinner at precisely 6:30. © 2012 QualPro

preconceived adj—already thought of Yankees have many preconceived ideas about Tennesseans: illiterate, barefoot moonshine makers who marry their cousins. previous adj—that which came before; preceding The receipt from the previous customer was still in the ATM when I got my cash. progressive adj—socially or culturally different from a mainstream idea Darcy’s kids go to a progressive school that does not divide students into grades. quasi- prefix—sort of; somewhat The roller coaster made Jenna quasi-queasy, but she still felt like riding the Ferris wheel. quintessential adj—the absolute basic Superman is the quintessential superhero: he has a mysterious origin, amazing powers, and one peculiar weakness. randomly adv—not in any predictable order The winning numbers on the Draw Five lottery are supposed to come out of the machine randomly, not in order. rational adj—based on thought, not feeling; reasonable Officer Hayes always stays rational, even when the victims and suspects appear crazy. redundancy n—words that are unnecessary because they have been stated in another way The phrase “3 a.m. in the morning” uses an obvious redundancy. redundant adj—unnecessary because they have been stated in another way The phrase “12 midnight at night” is redundant. reinforce vt—to make stronger Seeing Ron’s vanity license plate, which said “STUDLY,” reinforced my belief that he was conceited. relevant adj—related to the important idea In determining a woman’s fitness, her height is relevant to her weight. reluctantly adv—not wanting to The day after she got her braces, Taylor went reluctantly to school. © 2012 QualPro

remnant n—leftover piece Mama made a Kayce a doll’s dress out of the remnant of the white satin she used for Gail’s wedding gown. remote adj—away from everything else Don refused to stay in a Holiday Inn; he wanted a remote inn, far away from the shopping areas. replenish vt—to fill back up; to restore to its original volume Because Trace replenished the whiskey bottle with tea, it looked like no one had drunk any. resemblance n—“looking-alike-ness” Steve’s resemblance to Stephanie made many people think they were brother and sister. resistant to adj—able to avoid being infected or taken in by Davy’s mom need to find clothes that are resistant to mud, tears, and being left behind. resolution n—strength of will Bertha’s resolution to avoid desserts was strong enough to survive five birthday parties. resonate vi—to spread a sound or an idea The thumps from Dwight’s car stereo resonated into Mrs. McGregor’s bedroom. resources n—qualities or material that can be used Even my mostly worthless brother has resources: his stomach makes a good pillow, and I can light a match on his unshaved chin. respectively adv—in the same order as the items on the other list Horn-rim glasses, platform shoes, and fedoras are fashionable accessories that have been recycled from, respectively, the Twenties, the Seventies, and the Fifties. revel v—to enjoy indulgently After six months at sea, the sailors reveled for three days in everything New York had to offer. reverent adj—treating with great respect, as if holy Andrew is usually hyper, but he was almost reverent at the Air and Space Museum, because he wants to be an astronaut. © 2012 QualPro

revisionist adj—trying to change the accepted idea Since she was always old school, Prof. Wallace fought against the revisionist movement. rift n—a space that divides After three months of harmony, the roommates developed a rift over Fred’s new girlfriend. rudimentary adj—just enough to get by Dad threw together a rudimentary meal of crackers, cottage cheese, and applesauce. sacrilege n—a supreme insult to something held holy My uncle, the chef, thinks using Cool Whip instead of freshly whipped cream is a sacrilege. sanctuary n— 1. a place that provides protection and safety because it has been set aside by a religious authority Most weddings are held in the sanctuary of a church. 2. the status of someone who depends on the protection of a sanctuary In The Hunchback of Notre Dame, the gypsy girl found sanctuary in the cathedral. sapling n—a young tree The gardener had to prop up the maple sapling with ropes and stakes. satellite n—something that orbits around something else The moon is a satellite of the Earth, and photographers are satellites of Jennifer Lopez. saturation n—being so full that it is impossible to hold any more The advertisers created complete saturation of the media by running ads for the new candy bar in every TV station, every magazine, and every radio station. scholarly adv—like someone who enjoys school; academic; bookish My teacher wants us to use scholarly articles, not just whatever we find on Google. scrutinize vt—to examine closely Aunt Nelda found a great deal by scrutinizing the want ads every day. scrutiny n—careful observation Mr. Pierre puts every wedding gown through close scrutiny before each bride arrives. © 2012 QualPro

seascape n—a painting or drawing of the sea and features in it or nearby; compare to landscape While we were walking on the beach, we met an artist who was painting a seascape. seemingly adv—apparently; giving the appearance of Myra was seemingly calm, although she had just been in a car wreck. selectively adv—in a picky, careful way Aunt Reba always chooses her fruit selectively; she never buys the big bag. seminal adj—a basic part of what comes after The invention of the wheel was seminal to most forms of transportation. sensory adj—having to do with seeing, hearing, tasting, smelling, or feeling (as opposed to thinking) Good writers use lots of sensory details, like “velvety,” “granite-hard,” and “coal-black.” sentiment n—an expression of feeling; an opinion colored by emotion Sara could not find a card with the right sentiment after she let the Smiths’ cat run away. serenity n–the state of being serene: beautifully calm After a week in the city, the serenity of the woods was just what I needed. shrill adj—high, piercing, and grating on the ear Everyone on the playground knew Ms. Skelly’s shrill, demanding voice. shrub n—any bushy plant, smaller than a tree, often used for decoration or as a fence Uncle Billy always hides the Easter egg with the five-dollar bill in the shrub by the back door. shun vt—to avoid deliberately and systematically All the girls in Ms. Knowles’ class shunned Renee after she tattled on them. simultaneous adj—occurring at the same time The fireworks show timed the starbursts so that they were simultaneous with the music. singular adj—unusual; not like anything else Adele won several Grammy Awards because of her singular, throaty voice. site n—a place where something happened or is planned to be People kept staring at the site of the wreck, even though it had been cleaned up. Note: do not confuse with cite © 2012 QualPro

sit-in n—a form of protest in which participants sit in a targeted place until their demands are met. Many civil rights protesters held sit-ins at the drugstore counters where they were forbidden to sit because of their race. sizable adj—big After he caught the burglar, Officer O’Leary got a sizable reward. skepticism n—tendency to doubt Uncle Don’s skepticism about the weather report explains why he takes his umbrella. slogan n—a saying that identifies a movement or person During the Fifties, “I Like Ike” was the slogan on buttons that Eisenhower supporters wore on their skinny lapels. social order n—“the way things are”; the unwritten rules for how a society works The social order of the Fifties did not allow women to have a career and a family. solace n—emotional comfort After Mark broke up with her, Lana found solace by learning tae kwon do. sovereign adj—all-powerful; in control of the entire unit King Henry VIII gained the sovereign power over the English by forming the Church of England. specific adj—exact; of a particular kind My irritating brother always has to choose specific potato chips; he can’t just reach in and grab. speculate vi—to invest money or ideas in something you aren’t sure about; to gamble Uncle Reggie speculated on gold, hoping the price would continue to rise. spin-off n—a TV show originated as a feature of another TV show The Andy Griffith Show was a spin-off of an episode of The Danny Thomas Show in which Danny gets a speeding ticket driving through a poky Southern town. stable adj—staying the same; neither getting better nor worse After the accident, the doctors said DaShawn’s condition was stable enough for him to go home. © 2012 QualPro

stationary adj—staying in one place All of the furniture in the Lanes’ living room is stationary except the rolling coffee table. Note: do not confuse with stationery stationery n—specialized, fine quality paper for writing letters and notes My mother always uses monogrammed stationery for writing thank-you notes. Note: do not confuse with stationary status n—current state of being On the medical report, Jenna claimed her marital status was “married.” steerage n—the lowest level of a passenger ship, where those buying the cheapest tickets stay The passengers in steerage rarely socialize with the first-class passengers. stereotypical adj—matching what people expect because of one trait Dr. Barbie Strickland, the astrophysicist, is not a stereotypical “dumb blonde.” stifle vt—to repress; to hold down The speech was boring, but I had to stifle all my yawns because I was sitting on the stage. subjective adj—based on feelings and not on fact Dr. Lyles was being a little subjective when he said broccoli was “yucky.” succession n—a series She established her star status by a succession of wildly popular movies. succumb vi—to fall a victim (to) After fighting it for five years, Mrs. Norris finally succumbed to cancer and died last night. superficial adj—only on the surface; not deep Even though the car was totaled, Manny’s wounds were only superficial. superimpose vt—to lay (something) on top of something else If you superimpose a geological map on top of the street map, you can see why May Street is a dead end; it’s practically on the edge of a cliff. sustenance n—that which sustains; the stuff that keeps something alive Sylvester the Cat justifies his attempts to eat Tweety Bird by saying, “I’m in need of sustenance.” © 2012 QualPro

syndicated adj—a group of similar businesses owned by one company Most newspapers are syndicated, although a few are still independently owned. syringe n—a device for putting a small amount of a liquid into a small space, like a medicine into a vein, in which a tube with a closed end is pushed inside a tightly fitting tube with a narrow opening at the end, usually attached to a hollow needle through which the liquid is delivered I stared at the syringe on the tray in front of me, waiting for the dentist to return. taut adj—tightly stretched Sam made the sides of the tent so taut that you could bounce a nickel off them. taxed with vt—given the responsibility for Now that Mindy has moved back home with her baby, her parents are taxed with two mouths to feed. tenet n—any opinion , principle, or doctrine that a person or group holds One of the tenets of the Boy Scouts is “Be prepared.” terra firma n—Latin for “solid earth” I loved flying in the helium balloon, but I admit I was glad to get back to terra firma. terrestrial adj—having to do with the earth A farmer’s interests are mainly terrestrial, while a sailor prefers the water. theorize vi—to propose an explanation for In the ancient world, philosophers theorized that maggots came from dead flesh. thereafter adv—from then on; starting at that point and then going on Max likes to eat all the meat off the bone and thereafter to bury the bone in the garden. thus adv— 1. like this; in this way To curl paper ribbon, hold it thus: with your thumb on top of the ribbon and a scissors blade underneath. 2. therefore; because of what has just been said I had seven slices of pizza; thus, I didn’t really want dessert. timber n—trees that have been felled and are to be used for wood for furniture, paper, etc. Oregon and Washington provide much of the timber for America’s wood. © 2012 QualPro

tirade n—a long speech in which the speaker fusses or complains When twenty out of twenty-seven students failed the test, Mr. Dorris went into a long tirade about studying. toxin n—a poison that comes from a plant or animal Some mushrooms contain a toxin called coprine, which causes hangover-like symptoms. trajectory n—the curved path of something hurtling through space The trajectory of the bullet proved it could not have come from the policeman’s gun. transcend vt—to go beyond or above Being voted Most Valuable Player transcended Philip’s dreams of making the team. transition n—a graceful easing from one thing to another I hope Kelsey can make the transition from being an only child to living in a dormitory. translucent adj—able to let light through but diffusing it enough to conceal any object behind it The fogged-up windshield was too translucent for me to drive. treason n—an act of betrayal against one’s own country Benedict Arnold is famous for his act of treason, betraying the United States to England. typesetting n—the art of placing tiny metal letters and numbers in place to be covered with ink and pressed against paper to make a printed page Now that many homes have their own laser printers, the art of typesetting is threatened. tyranny n—any government controlled by a single person “Taxation without representation is tyranny” was the rallying cry of the American revolution. tyrant n—one who has absolute power over a country Mussolini, who later joined forces with Hitler, was a tyrant over Italy in the 1930s. uncanny adj—“un-explainable”; something for which no one knows the reason Chester was afraid to spend the night in his aunt’s old house because of the uncanny noises in the wall. unparalleled adj—unmatched; too extreme to be equaled Michael Phelps’ unparalleled number of Olympic gold medals has won him a place in history. © 2012 QualPro

unprecedented adj—original; having nothing similar that came before Franklin D. Roosevelt ran for an unprecedented third term as president—and then a fourth! unsolicited adj—“un-asked-for” I’m thinking of putting a trash can beside the mailbox for all those unsolicited advertisements. urgency n—need for action When I understood the urgency of your need, I rushed right over. urn n—a large vase, sometimes with a lid My Aunt Frieda ‘s favorite possession is a Chinese urn made of carved yellow jade. vaccine n—a preventive medicine made from the disease-causing essence itself; by introducing a small amount of the germ into the body, the body forms antibodies to fight the disease, and can thus resist further exposure to the disease. Louis Pasteur’s vaccine against anthrax saved millions of cows from dying. vindicate vt—to prove innocent after having been blamed If Zia swells up after eating that peanut butter sandwich, she will be vindicated against the suspicion that she has been sneaking peanuts every night. visionary n—one who imagines how the future can be Someone said that all children are visionaries, and all old men are historians. vivid adj—strongly colored; standing out from the background A report of three drive-by shootings in one week was a vivid reminder of the crime rate. voluptuous adj—heavily fleshed in a beautiful way Francesca was pretty and voluptuous enough to be a model for Lola’s Large Lady Fashions. vulnerable adj—easily wounded or hurt Even a big guy like Bruno is more vulnerable after a breakup with a girl like Vanessa. wherefore conj—why; for what reason When Juliet says, “Wherefore art thou Romeo?” she is asking why the only boy she has ever loved has to be one of her family’s enemies, not “Where are you, sweetie?” © 2012 QualPro

whimsy n—a lighthearted, playful attitude If you like whimsy, you’ll love Alice in Wonderland. withdrawn adj—shy; staying away from people The poor abused dog was withdrawn until Jamie gave it some food. worldview n—an overall way of looking at the world Hitler’s worldview was that the “right people” should control the world. Irregular Plurals antenna, antennae axis, axes criterion, criteria datum, data focus, foci matrix, matrices millennium, millennia nucleus, nuclei radius, radii thesis, theses vertex, vertices Most of these words taken from the five practice tests in The Real ACT Prep Guide, 3rd Ed. © 2012 QualPro

Appendix 2 ACT Math Concepts and Problems

Math Vocabulary area of a circle chord circumference collinear
complex number congruent consecutive diagonal directly proportional endpoints function y = R (x) hypotenuse integer intersect irrational number least common denominator logarithm matrix mean median obtuse perimeter perpendicular pi polygon prime number quadrant quadratic equation quadrilateral quotient radian radii radius rational number real number slope standard coordinate plane transversal trapezoid vertex x-intercept y-intercept

Math Vocabulary √ area of a circle—A = π r2
chord—a line drawn from the vertex of a polygon to another non adjacent vertex of the polygon circumference—the perimeter of a circle = 2 π r collinear—passing through or lying on the same straight line complex number—is an expression of the form a+bi, where a & b are real numbers and i2 = -1 congruent—corresponding; equal in length or measure consecutive—uninterrupted sequence diagonal—a line segment joining two nonadjacent vertices of a polygon or solid (polyhedron) directly proportional—increasing or decreasing with the same ratio endpoints—what defines the beginning and end-of-line segment Function y = R (x)—a set of number pairs related by a certain rule so that for every number to which the rule may be applied, there is exactly one resulting number hypotenuse—the longest side of a right-angle triangle, which is always the side opposite the right angle integer—a member of the set ..., -2, -1, 0, 1, 2, … intersect—to share a common point irrational number—cannot be expressed as a ratio of integers, eg., , π, etc. least common denominator—the smallest number (other than 0) that is a multiple of a set of denominators (for example, the LCD of ¼ and ⅓ is 12) logarithm—log a x means ay = x matrix—rows and columns of elements arranged in a rectangle mean—average; found by adding all the terms in a set and dividing by the number of terms median—the middle value in a set of ordered numbers obtuse—an angel that is larger than 90° √ 3

Math Vocabulary (continued)
perimeter—the distance from one point around the figure to the same point perpendicular—lines that intersect and form 90-degree angles pi— = 3.14 … polygon—a closed, plane geometric figure whose sides are line segments prime number—a positive integer that can only be evenly divided by 1 and itself quadrant—any one of the four sectors of a rectangular coordinate system, which is formed by two perpendicular number lines that intersect at the origins of both number lines quadratic equation—Ax2 + bx + C = D, A ≠ 0 quadrilateral—a four sided polygon quotient—the result of division radian—a unit of angle measure within a circle radii—the plural form of radius radius—a line segment with endpoints at the center of the circle and on the perimeter of the circle, equal to one-half the length of the diameter rational number—r can be expressed as r = where m & n are integers and n ≠ 0 real number—all numbers except complex numbers slope—m = standard coordinate plane—a plane that is formed by a horizontal x-axis and a vertical y-axis that meet at point (0,0) (also known as the Cartesian Coordinate Plane) transversal—a line that cuts through two or more lines trapezoid—a quadrilateral (a figure with four sides) with only two parallel lines vertex—a point of an angle or polygon where two or more lines meet x-intercept—the point where a line on a graph crosses the x-axis y-intercept—the point where a line on a graph crosses the y-axis m n y2 – y1 x2 – x1

Math Section Content Pre-algebra Elementary algebra
Intermediate algebra Coordinate geometry Plane geometry Trigonometry Miscellaneous topics Math test-taking strategy

Pre-Algebra – Word Problems
Converting a word problem into an equation: If a discount of 20% off the retail price of a desk saves Mark $45, how much did Mark pay for the desk?

Pre-Algebra If a discount of 20% off the retail price of a desk saves Mark $45, how much did Mark pay for the desk? Amount Paid (Sales Price) = Retail Price – Discount Discount = 20% × Retail Price $45 = 20% × Retail Price Retail Price = $45/.2 = $225 Sales Price = $225 − $45 = $180

Pre-Algebra A lawn mower is on sale for $1600. This is 20% off the regular price. How much is the regular price?

Pre-Algebra A lawn mower is on sale for $1600 which is 20% off the regular price. How much is the regular price? Sales Price = Regular Price – Discount Discount = 0.20 × Retail Price Sales Price = Regular Price – 0.20 × Retail Price $1600 = 0.80 × Regular Price Regular Price = $1600 / 0.8 = $2000

Pre-Algebra If 45 is 120% of a number, what is 80% of the same number?

Pre-Algebra If 45 is 120% of a number, what is 80% of the same number?
45 = 1.2 (X) X = 45/1.2 = 37.5 Y = 0.8 (37.5) = 30

Elementary Algebra – Substitution, 2 Equations, 2 Unknowns
If a – b = 14, and 2a + b = 46, then b = ? a = 14 + b; substitute 2(14 + b) + b = 46 28 + 2b + b = 46 3b = 18 b = 6, a = 20

Elementary Algebra a c + = (a + c) / b + = (ad + bc) / bd b b a c b d
3x3 + 9x2 – 27x = 0; 3x (x2 + 3x – 9) = 0 (x+2)2 = (x+2)(x+2) (x/y)2 = x2/y2 X0 = 1

Intermediate Algebra – Quadratics
x2 + 3x – 4 = y x2 + 3x – 4 = 0 Factoring: (x – 1) (x + 4) = 0 X = 1, -4 For ax2 + bx + c = 0, the value of x is given by: X= (-3 + (32 – 4*1*-4).5)/2 = 1 X= (-3 - (32 – 4*1*-4).5)/2 = -4 Quadratic Formula

Intermediate Algebra – Factoring Polynomials, Solve for x
x2 - 2x = 0 (x - 5) (x + 3) = 0 x = 5, -3

Intermediate Algebra – Factoring Polynomials
Example 1 Example 2 x3 + 3x2 + 2x + 6 (x3 + 3x2) + (2x + 6) x2(x + 3) + 2(x + 3) (x + 3) (x2 + 2) x3 + 3x2 + 2x + 6 / (x + 3) ((x3 + 3x2) + (2x + 6)) / (x+3) (x2(x + 3) + 2(x + 3)) / (x+3) ((x + 3) (x2 + 2)) / (x+3) x2 + 2

Intermediate Algebra – Exponents
x3 * x2 = x5 x9 / x2 = x7 (x2)5 = x10 1/x4 = x-4 x2 * x.5 = ? x4 / x8 = ? (x.5)2 = ? 1/x-z = ? x2 * x.5 = x2.5 x4 / x8 = x-4 (x.5)2 = x 1/x-z = xz

Intermediate Algebra – Imaginary Numbers

Coordinate Geometry – Coordinates Equation of a Line
y = mx + b, equation of a linear (straight) line m = slope of the line = change in Y / change in X b = y intercept If m is negative, the line is going down and if positive the line is going up (left to right). What is the equation for the line between points, (1, -2) & (6, 8)? m = change in y values / change in x values = (y1 – y2) / (x1 – x2) m = [8- (-2)] / (6 - 1) = 10/5 = 2 b = y – mx; b = 8 – (2) × (6) = 8 – 12 = -4 y = 2x -4

Coordinate Geometry – Coordinates
What is the distance between these points (-1, 2) and (6, 8)?

Coordinate Geometry – Coordinates
What is the distance between these (-1, 2) and (6, 8)? * 6, 8 c b 6 a * -1, 2 7

Plane Geometry Lines and Angles Triangles Circles
Squares and Rectangles Multiple Figures

Opposite (vertical) angles are congruent (equal)
Plane Geometry: Lines c abc + cbd = 1800 a d b a b d c Opposite (vertical) angles are congruent (equal) All angles combined = 3600 Transversal line thru two parallel lines creates equal opposite angles.

Plane Geometry: Triangles

Plane Geometry Area of a triangle = ½ (base * height) The sum of the three angles = 1800 Area of a trapezoid = ½ (a +b)*(height) where a and b are the lengths of the parallel sides Diameter = 2 * radius of a circle Volume of cylinder = area of circle * height a b r h

Plane Geometry Example
What is the area of the square if the radius equals 5? L L r Diameter = 2 x r The diameter = 1 side of the square Area = L x L Diameter = 10 (same as a length of a side), Area = 100

Plane Geometry Parallelogram
Area = Base x Height h b Note a rectangle is a parallelogram. The sum of the angles = 3600

Plane Geometry Circles

Plane Geometry Circles
What is the equation of these circles? (x-1)2 + y2 = 1 (x-3)2 + (y-1)2 = 4

Plane Geometry Terms Congruent = equal lengths
Co-linear = on same line abc = the angle of b in the triangle abc Acute = less than 90 degrees (A cute little angle) Obtuse = greater than 90 degrees

Trigonometry For all right triangles H O 90° Memory Aid t A
SOH CAH TOA sin (t) = sine t = cos (t) = cosine t = tan (t) = tangent t = cot (t) = cotangent t = t A opposite side O = hypotenuse H adjacent side A hypotenuse H opposite side O adjacent side A 1 adjacent side A = tangent t opposite side O

Trigonometry H O t A H2 = A2 + O2

Trigonometry H O t A Tan (t) = O/A
if O = 2 and A = 2, then O/A = 2/2 = 1 Tan (t) = 1 H O t A H2 = A2 + O2

Miscellaneous Topics – You May See These On The ACT Math
Fundamental Counting Principles 3 shirts, 2 pairs of pants, 4 sweaters – how many days with a different outfit? (3)(2)(4) = 24 day of a unique combination How many different and unique phone numbers of a 7 digit number? (10)(10)(10)(10)(10)(10)(10) = 107

Miscellaneous Topics – Probabilities – Examples
Given: 5 red marbles are placed in a bag along with 6 blue marbles and 9 white marbles: Question: if three white marbles are removed, what is the probability the next marble removed will be white? Originally, there were 9 white marbles out of 20; with 3 white marbles removed, there are 6 out of 17 remaining. The probability the next marble removed is white = 6/17. Question: if 4 blue marbles are added to the original amount, what is the probability the first marble removed is NOT white? Now there are 24 marbles total with 15 non-white. The probability that the first marble removed is not white is 15/24.

QualPro Recommendations for

Similar presentations

Presentation on theme: "QualPro Recommendations for"— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

QualPro Recommendations for

Similar presentations

Presentation on theme: "QualPro Recommendations for"— Presentation transcript:

Similar presentations

About project

Feedback